A unity feedback system has a forward transfer function as shown in Figure 3(a). K Rís)- Glo)- T+1Xs+4Xs +S) Y(s) Figure 3(a) (6) Determine the loop transfer function of the system. Calculate the angles of asymptotes, crossing point of asymptotes, breakaway point and jo-axis crossing. Consequently, sketch the root locus of the system for K 20. (i) (iii) Based on the root locus in 3(a)(ii), evaluate the system response as K increases from 0 to +o. Justify your answer.

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(a)
A unity feedback system has a forward transfer function as shown in Figure 3(a).
K
R(s)
G(s)=
Y(s)
(+)Xs+4Xs+5)
Figure 3(a)
(i)
Determine the loop transfer function of the system.
(ii)
Calculate the angles of asymptotes, crossing point of asymptotes,
breakaway point and jo-axis crossing. Consequently, sketch the root locus
of the system for K 20.
Based on the root locus in 3(a)(ii), evaluate the system response as K
increases from 0 to +to. Justify your answer.
(iii)
(b) The transfer function of a unity feedback control system is given as,
K(1 + 0.2s)
s(s + 2)(s2 +s+ 1)
G(s)
(i)
Sketch the Bode Plot for the system for K= 1.
Estimate the system's gain margin and phase margin based on the Bode
Plot in 3(b)(i).
(ii)
Transcribed Image Text:(a) A unity feedback system has a forward transfer function as shown in Figure 3(a). K R(s) G(s)= Y(s) (+)Xs+4Xs+5) Figure 3(a) (i) Determine the loop transfer function of the system. (ii) Calculate the angles of asymptotes, crossing point of asymptotes, breakaway point and jo-axis crossing. Consequently, sketch the root locus of the system for K 20. Based on the root locus in 3(a)(ii), evaluate the system response as K increases from 0 to +to. Justify your answer. (iii) (b) The transfer function of a unity feedback control system is given as, K(1 + 0.2s) s(s + 2)(s2 +s+ 1) G(s) (i) Sketch the Bode Plot for the system for K= 1. Estimate the system's gain margin and phase margin based on the Bode Plot in 3(b)(i). (ii)
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